Mühendislik Fakültesi Koleksiyonu
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Item A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials(NATL INQUIRY SERVICES CENTRE PTY LTD, 2019) Küçükoğlu, İrem; Şimşek, Yılmaz; Srivastava, H. M.The aim of this paper is to investigate some classes of higher-order Apostol-type numbers and Apostol-type polynomials. We construct Lerch-type zeta functions which interpolate these numbers and polynomials at negative integers. Moreover, by combining some well-known identities such as the Chu-Vandermonde identity with the Lerch-type zeta functions and generating functions for the higher- order Apostol-type numbers and Apostol-type polynomials, we derive some relations and identities including functional equation for these Lerch-type zeta functions with other zeta type functions, Raabe-type multiplication formula for the higher-order Apostol-type polynomials and the Stirling numbers. Finally, we give some remarks and observations on Lerch-type zeta functions and their functional equations.Item Some approximations with hurwitz zeta function(UNIV NIS, FAC SCI MATH, 2020) Aygüneş, Aykut AhmetIn this paper, we focus on some approximations with Hurwitz zeta function. By using these approximations, we present some asymptotic formulae related to Hurwitz zeta function. As an application, we give two corollaries related to Bernoulli polynomials.Item A note on polylogarithms and incomplete gamma function(UNIV BELGRADE, FAC ELECTRICAL ENGINEERING, 2020) Aygüneş, Aykut AhmetIn this paper, we firstly introduce the polylogarithms and incomplete gamma function. Then, we claim that there is a relation between polylogarithms and a generalization of incomplete gamma function. Secondly, we give a formula related to polylogarithms. Also,we obtain a relation between incomplete gamma function and the derivatives of polylogarithms. Finally, we find a generating function for the values of incomplete gamma function.Item Let me make mathematics and music together: A meta-analysis of the causal role of music interventions on mathematics achievement(ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD, 2023) Akın, AyçaThis research aims to conduct a fixed-effects meta-analysis to unpack the causal role of music interventions on mathematics achievement. Findings indicated that music interventions had a small to moderate positive effect on mathematics achievement (N = 77,595, k = 245, g = 0.36, p < 0.01, 95% CI [0.34, 0.38]). Mathematics skills, instructional mathematical content, types of music interventions, and age were significant moderators, whereas development status was not a significant moderator for this meta-analysis. The most crucial result was that studies using music-mathematics integrated intervention produced a large effect size. This study can be considered interesting in terms of revealing that a significantly strong and positive transfer in mathematics learning was only achieved when used mathematics and music together in the learning environment. Consequently, the current research is regarded to have laid some groundwork for further meta-analytic investigations as it provides detailed, up-to-date, and useful evidence on this issue.
